Statistical Design of Fender

8/21/2019 Statistical Design of Fender

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Statistical Design of Fender for Berthing Ship

Shigeru Ueda

Tottori University, Tottori, Japan

Toshihiko Hirano

Tottori University, Graduate School, Tottori, Japan

Satoru Shiraishi, Shuji Yamamoto

Independent Administrative Port and Airport Research Institute, Kanagawa, Japan

Seigi Yamase

Bridgestone Corporation (Yokohama Factory), Kanagawa, Japan

ABSTRACI

Fender is commonly used for the purpose to absorb berthing energy

and to decrease impact of berthing ship. Ships berthing energy is

proportional to virtual mass of ship and square of approach velocity,

however it was reduced by rotational motion caused by eccentric

berthing. Currently, fender is designed by calculating berthing energy

for the maximum size ship and/or standard size ship considering ship

mass, virtual mass factor, design approach velocity and eccentricity

factor. Then select suitable fender to absorb ships berthing energy.

Recently, ship size increases so fast. For instance, size of modem

container ships became more than 100,000 DWT. At some port, no

berth is constructed to meet above those ships in full laden. As the

result, ships larger than design ship is to be obliged lightening its draft

at berthing. Even if the berth water depth is secured, virtual approach

velocity must be decreased than design approach velocity.

Some of the present authors had attempted to design a fender for

berthing ship by means of statistical method and presented the results

of the analysis to the llth ISOPE (Ueda and et al 2001). While in the

previous paper, the probability of failure and safety factor on fender

design for container ships were calculated, in this paper, analysis was

made for conventional cargo ships by use of statistical data of arriving

ships in some major port in Japan.

KEY

WORDS:

rubber fender, statistical design, berthing ship,

approach velocity, ship displacement, virtual mass factor, eccentricity

factor

1. INTRODUCTION

When ships berth for loading and unloading, fender is used fo

the purpose to absorb berthing energy and to decrease impact o

berthing ship. Because of its purpose, fender should be designed tha

ships berthing energy does not exceed energy absorption of fender.

Ships berthing energy is calculated for the maximum size shi

and/or standard size ship considering ship mass, virtual mass factor

design approach velocity and eccentricity factor. But ship size

generally registered by dead weight tonnage

(DWT)

for container ships

cargo ships and others. Therefore, those factors necessary in calculation

of berthing energy such as ship mass, virtual mass factor, design

approach velocity and eccentricity factor are to be derived from

D WT.

In the current Design Standard for Port and Harbour Facilities

Japan (1999), factors concerning berthing energy are determined

accordance with either 75% or 95% confidence level.

As those factor

are not fixed but variable, and different for those entrance ships of sam

DWT, there is a possibility that ships berthing energy exceed th

energy absorption of design fender.

In this paper, all factors were treated as variable. And th

probability of failure of fender designed according to the current design

standard was calculated by statistical method. Then the authors wi

propose the statistical design method of fenders for berthing ships.

2. PROCEDURE OF THIS STUDY

In this study, fender is designed by statistical method as follow

(refer to Figure-l).

@ Give ship size

D WT

for analysis.

Proceedings of The Twelfth (2002) International Offshore and Polar Engineering Conference

Kitakyushu, Japan, May 2631, 2002

Copyright 2002 by The International Society of Offshore and Polar Engineers

ISBN 1-880653-58-3 (Set); ISSN 1098-6189 (Set)

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Analyze the relation between

DWT

and V,(approach velocity),

C,(virtual mass factor), C,(eccentricity factor). Then, calculate

those values such as

V,,,

C,,,, C,. (see section 3.1)

Analyze Z the ratio of energy absorption of fender against

catalogue value

Ecu,.

Then, obtain the energy absorption of design

fender Ef (see section 3.2)

Obtain ships berthing energy Es.

Compare the ships berthing energy

Es

and the energy absorption

of design fender Ey

Calculate the probability of exceedance of the ships berthing

energy over the energy absorption of design fender. (see section

4)

Calcu1at.e the energy absorption of fender and the safety factor

which satisfies the required probability of exceedance.

Figure-l Procedure of This Study

Where, specified failure function G is defined as following equation.

G=E, -Es

E,: Energy absorption of fender, E,: Ships berthing energy

Z Fender factor, EC,,: Catalogue value

M Ships mass (Displacement tonnage), V,: Approach velocity

C,: Virtual mass factor, C,: Eccentricity factor

1)

3. CHARACTERISTIC OF FACTORS CONCERNING

FENDER DESIGN

3.1 Factors Concerning Ship s Berthi ng Energy (Ueda et al. 2001)

In this chapter, the relation is shown between DWT and factors of

ships berthing energy. All factors such as ship mass, approach velocity,

virtual mass factor, eccentricity factor are treated as random variables.

Those values are regressed to linear on co-natural logarithms

And it is assumed that those values above mentioned as normally

distributed on regression lines (refer to Figure. 2).

In this study, object of analysis is not only a container ship b

also a cargo ship. Therefore the relation between

DWT

and

DT a

shown for container ships and cargo ships. The relation between

DW

and other factors concerning energy absorption of fender were alread

presented in the paper submitted to the llth ISOPE, however thos

relations are shown again (Figures.4-6).

Design Ship Size

ln DWT)

Figure-2 Explanation of Relation between DWT

and Factors of Ships Berthing Energy

a) Ship Mass (Ship Di splacement Tonnage), DT

Figure-3 shows the relation between DWT and displacement

tonnage

DT

for ships listed in Lloyd Registered of Shipping an

Registered Ship in Japan analyzed by Akakura and et al. (1998). This

the relation of container ship for ships full laden.

200,000

5

& 150,000

3

r

2 100,000

E

8

m

.g 50,000

.P

a

0

-I

0

20,000 40,000 60,000 80,000 100,000 120,000

Dead Weight Tonnage (DFV)

0

- 50% confidence

0 - 75% confidence

0

____ 90

confidence

@I I-~- 95% confidence

50 confidence DT =2.203.DWT0.

75 confidence DT =2.317.DWT3

90 confidence DT =2.425 .DWT s3

95 confidence DT =2.492.DWTQ

Figure-3 Relation between D WT and DT for Container Ship

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Regression Equations between DWT and DT for Cargo Ship under

10,OOODWT are as follows.

50 confidence DT = 3.327. D WTQ.899

75 confidence DT = 3.548. DWT.g99

2)

90

confidence DT = 3.767. D WT.899

95 confidence DT = 3.899. DWT.899

Regression Equations between

DWT

and DT for Cargo Ship over

10,OOODWT

re as follows.

50 confidence DT = 3.119. DWT.93

75% confiaence DT = 3.373. DWTa.93

(3)

90

confidence DT = 3.614. DWT.93

95 confidence DT = 3.767. DWT0.93

b) Approach Veloci V,

Ship shall touch the quay at either bow or stem at first impact,

then touch at the opposite side alternatively. According to the

observation by Moriya et al. (199 1 , it is found that approach velocities

in bow berthing are rather larger than those at stem berthing, however

there are several occasions in stem berthing which are rather larger than

those of at bow berthing. Therefore, analysis was made with the data

including approach velocities at bow and stem berthing, and the

relation between DWT and approach velocities was obtained as shown

in Figure-4.

0.25

g 0.20

x

; 0.15

s

f 0.10

41

8 0.05

0.00

(j) ~ 50% confidence

@ - 75% confidence

(3 - 90% confidence

@ ,--x~.- 95% contidence

9

\

50%cotidence V, =1.925.DWT~.*

@&- 75%conftience Vb=2.422.DWTmo338

90%confdence V, = 2.977. DwTm338

95%mnfiience V, =3.369. DWlmo.8

0 10000 20000 30000 40000

50000

Dead Weight Tonnage (D WT)

Figure-4 Relation between

D

WT and

V,

c) Vi rtual Mass Facto*, C,,,

Virtual mass factor is calculated by means of Uedas formula

(1981) for those ships listed in Lloyd Registered of Shipping and

Registered Ship in Japan. Figure-5 shows the relation between DWT

and virtual mass factor.

c, =l+Lxd

2C, B

(4)

Where,

C,: Virtual mass factor, C,: Block coefftcient

d: Full load draft, B: Breadth extreme

ah----

50% confidence

@----

90% confidence

@ - 75% confidence

@ -..95% confidence

2.2

50%confidence C,=1.490~DCYT0.**

75% confidence C =1.527~DcYT~0218

90%confidence

cl cl.56 1.DwP8

95 %confidence

c, =1.68 1~DwP*

0

20,000 40,000 60,000

80,000

100,000 120,000

Dead Weight Tonnage (D WT)

Figure-5 Relation between DWT and C,

d) Eccentr icity Factor, C,

Eccentricity factor is given by the following formula which

derived considering energy dissipation after the berthing with t

rotational motion around the contact point either at bow or stem. B

use of those data above mentioned, the relation between

DWT

a

eccentricity factor is obtained as follows.

1

ce = 1 + z/u)

Where,

I: the distance from the contact point to center of gravity of berthin

ship measured parallel to the quay line

r: radius of gyration

CD----

50% confidence

@ - 75% confidence

0 -- 90% confidence @ ^.~.I.. I.~5% confidence

0.60 ,

1

a 0.55

B

d

.& 0.50

2

I2 0.45

fi o.40 iiii. ~~~~~

0 20,000 40,000 60,000 80,000

100,000 120,000

Dead Weight Tonnage (DWT)

Figure-6 Relation between

D WT

and C,

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3.2 Factor Concerning Energy Absorption

Fender factor Z is the factor of energy absorption of fender

against catalogue value Ecar For instance, factor Z4.0 means that the

energy absorption of fender is equal to that of catalogue value and

ZxO.9 is regarded to 10% reduction to E,,,. Probability density function

fit well to normal distribution of which mean ~~0.997 and standard

deviation d z= 0.03 1 as shown in Figure-7.

Measured Value

II Normal Distribution

Fender Factor Z

Figure-7 Frequency Distribution and Expectation of Factor 2

4. PROBABILITY OF EXCEEDANCE FOR THE

CURRENT DESIGN METHOD

4.1 Example

of

Designed Fender

In this chapter, probability of exceedance was calculated for

designed fender by current method.

Fender was designed in cases where those values of 75%, 90%,

95% confidence levels for those items concerning ships berthing

energy as ship mass, virtual mass factor and eccentricity factor. Table-l

lists the condition of each case and energy absorption of fender in each

case.

Table-l Examples of Designed Fender Capacity

vb

DT,C,,C,

Effective Fender Capacity (kNm)

(Confidence (Confidence

35,OOODWTII 5,000DWT11 5,OOODWT

Level)

Level)

Ibontainer Shill1 Cargo Shin 11Cargo Shin 1

I 75%

11 128.8 11

izi

4.2 Calculati on Method

Based on statistical characteristics of factors, probability

exceedance that the ships berthing energy excess the effectiv

designed fender capacity was calculated. Calculation method is t

following two methods.

(a) Monte-Calm Simulation

Random numbers of the statistical characteristics of factors abov

mentioned were occurred and simulated. Where, number of simulation

trial was 10,000. As an instance, Figure-8 (a)-(d) show the number

occurrence and theoretical probability distribution of ship mas

approach velocity, virtual mass factor, eccentricity factor f

35,000DWT

container ship.

3000

2500

2000

; 1500

2 1000

z

F+ 500

0

:

P

;:

El

:

z

z

,

z m

z

: :

m

z m E

:

(a) Frequency of Distribution of DT

3000

2500

2000

; 1500

2 1000

2

Lr, 500

0

(b) Frequency of Distribution of V,,

3000

2500

(c) Frequency of Distribution of C,

2500

2000

; 1500

5 1000

rA 500

0

(d) Frequency of Distribution of C,

Figure-8 Calculation Results of Each Random Number

(Des&r Shin Size 35.000DKContainer Shin)

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(b) Second-Moment Method

Factors concerning ships berthing energy are treated as

logarithmic normal distribution. However, if all factors concerning

specified failure function G are assumed normal distribution, meanp G

and standard deviation bG of specified failure function G is obtained

from the following equation.

Where,

,U G: mean of specified failure function G

c G: standard deviation of specified failure function G

bGo)=P,-

,~2F33.P4P5J2

p I: mean of Z, ,U z: mean of DT,

,U + mean of V,,

p 4: mean of Cm p 5: mean of C,

c I: standard deviation of E,,,,

d z: standard deviation of DT,

d 3: standard deviation of V,,

d I: standard deviation of C,,

c + standard deviation of C,

Therefore, probability of exceedance is calculated by the following

equation.

For example, when design ship size is 35,OOODWT container ship and

catalogue value of fender is 128.8kNm, mean and standard deviation

are calculated as p G =69.395kNm and c G =72.252kNm. Thus,

probability of exceedance is calculated as 0.168 by equation (8).

4.3 Result of Probabil i@ of Exceedance

(a) Probability of Exceedance for Container Ship

In case of container ship of 35,OOODWT, Figure-9 shows the

probability of exceedance that the ships berthing energy exceed the

energy absorption of designed fender calculated by means of two

methods.

From the results, results of those two methods i.e. Monte-Calro

simulation and Second-Moment method are different in case of low

probability of exceedance. This may be caused by the difference of

assumption of statistical characters, i.e. Monte-Calro simulation

assumed logarithmic normal distribution but Second-Moment method

assumed normal distribution. It is obvious that there is a different in th

foot of distribution (refer to Figure-lo). Factors concerning ship

berthing energy are assumed normal distribution on natural logarithms

i.e. logarithmic normal distribution. Therefore, logarithmic norma

distribution for Monte-Calro simulation is better than norma

distribution for Second-Moment method. As the result, hereafter th

analysis is made by Monte-Calro simulation. Where, fender factor Z

treated as variable.

0.20

0.1 5

x

ii

m

iii

::

UJ 0.10

>,

.e

z

2

9

CL

0.05

Monte-Cairo Simulation Second-Moment Method

V,=75% confidence

V,=90% confidence

V,,=75% confidence

,

V,=90% confidence :

DT,CM.cC DT,CM.Ce DT.Ch+,Ce

DT.CM.Ce DT.cM,Ce

DT.CM,Ce

75XcMlfidence 9C coniidence 95Uconfiden.x 75Xconfidence 9O confidence 95Xconfiden

level

level

level level

level level

Figure-9 Probability of Exceedance for 35,000DWT Container Ship

-Logarithmic Normal

Distribution

.mw+-Normal Distribution

Ships erthing nergy (kNm)

Figure-10 Ships Berthing Energy of 35,000DWT Container Ship

by Two Methods

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(b) Probability of Exceedance for Cargo Ship

Furthermore, the probability of exceedance is calculated for

cargo ships. Figure-11-12 show the results of probability exceedance

for cargo ship by Monte-Calro simulation.

Vh=75% confidence

. ..---*..

Vb=90? confidence :

Vb=95% confident

DT,Cm,Ce

DT,Cm,Ce

75%confidence

90%confidence

level

level

DT,Cm,Ce

95%confidence

level

Figure- 11 Probability of Exceedance for

5,000D WT

Cargo Ship

0.20 r-

-I

Vb=75% confidence

5 11 - . . . . . . . . .

x

Vb=90% confidence 1

a

,

0.00

I

DT,Cm,Ce

DT,dm,Ce

DT,Cm,Ce

75%confidence

90%confidence

95%confidence

level

level

level

Figure-l 2 Probability of Exceedance for 10,OOODWT Cargo Ship

From the results, when confidence level of approach velocity is

raised, probability of exceedance is lower than other factors. It is found

out that the ships berthing energy is most influenced by the approach

velocity. It is the reason that ships berthing energy is proportional to

square of approach velocity and standard deviation of approach

velocity is maximum value in those factors.

5. FENDER DESIGN OF STATISTICAL METHOD

It can be said that probability of exceedance is seemed rathe

high for the fender designed according to the current design method. I

this chapter, the energy absorption for the required probability

exceedance is calculated for container ship and cargo ship, and then th

safety factor against effective designed fender capacity according to th

current design method is calculated.

The safety factor is defined by the following equation.

E, =Z-EC,, >y-Ed

9)

Where,

E,: Guaranty energy absorption of fender (kNm)

Z Ratio of energy absorption of fender catalogue value EcO,

EC,,:

Catalogue value of energy absorption of fender

Eg

Effective designed fender capacity according to the current desig

method (kNm), y : safety factor

Effective designed fender capacity Ed is calculated in accordance

with the current design method by use of 75% confidence level for sh

size, virtual mass factor and eccentricity factor, and 95% confidence

level for approach velocity.

Calculation of the safety factor was made by the following

method.

0 Calculate the energy absorption of fender Ed, by use of curren

design method.

@ Calculate the catalogue value of fender.

(Ecat=y *EJ .Z)

@ Energy absorption of the selected fender is obtained as

EFZ*E,,,=

Y *EF

@ Then, design ship size (DWT) is converted to DT.

@ And, calculate ships berthing energy

E,

for each trial.

@ Compare

Ef

and

E,.

If

E>Ep

regard that ships berthing energ

exceed energy absorption of fender.

@ Count the number of such occurrence among 10,000 trial, an

obtain the probability of exceedance.

@ Change safety factor y and calculate energy absorption an

repeat the steps from @ to @ until energy absorption satisfie

the required probability of exceedance.

Figure-13 show the result for

35,000DWT

container ship. In ca

when the factor Z was fixed as 0.9, and Ed is calculated by use of Vb

confidence level and DT, C,, C, of 75% confidence level. The result

safety factor was already presented in the paper submitted to the 1

ISOEP. In this paper, safety factor is calculated when factor Z

variable too. Furthermore, analysis is made for cargo ships. Figures

14-15 show those results on the condition that Z is variable.

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..-a-- Safety Factor

Current 0.01 0.006 0.004 0.002

Design Required Probability of Exceedance

Figure-13 Energy Absorption and Safety Factor for Required

Probability of Exceedance (35,OOODWTContainer Ship)

a

2 600

Required Energy

-.-~---Safety Factor

[ 3.0

Current 0.01

0.006

0.004 0.002

Design

Required Probability of Exceedance

Figure-14 Energy Absorption and Safety Factor for Required

Probability of Exceedance (5,OOOOwTCargo Ship)

Required Energy -s--Safety Factor

Current 0.01 0.006 0.004 0.002

Design

Required Probability of Exceedance

Figure-l 5 Energy Absorption and Safety Factor for Required

Probability of Exceedance (10,OOODwT Cargo Ship)

2.5

2.0

;;

1.5 z

2

x

1.0 e

0.5

0.0

Figure-13-15 show the required energy and safety factor f

required probability of exceedance. For example, when require

probability of exceedance is 0.01, safety factor is about 1.4, i.e. energ

absorption of fender is required about 1.4 times energy of designed

fender by current method.

These results are shown the necessity that factors considering

design of fender are treated as variable and fender is designed b

statistical design method.

6. CONCLUSION

(1) Ships berthing energy is greatly influenced by approach velocity

This is the reason that berthing energy is proportional to square

approach velocity and standard deviation of approach velocity

is maximum value in those factors.

(2) Factors concerning berthing energy not fixed but variable. Thu

even if entrance ship is the same as design ship size, it is possible

that ships berthing energy exceed energy absorption of fender.

(3) When a fender is designed by current design method, it

necessary to consider the safety factor for fender design.

(4) In this study, it is suggested that factors considering design

fender are treated as variable.

(5) This must be said not only for fender design but also for planning

port facilities in consideration of movement of conditions such

increment of ship size.

ACKNOWLEDGEMENT

The authors express sincere appreciation to the Yokohama

Investigation and Design Offlice, Second District Port Construction

Bureau,

Ministry of Transport (Now, Ministry of Land an

Transportation) for their kind cooperation to analyze the approach

velocity.

REFERENCES

1.

Ueda Shigeru et al (2001): Statistical Design of Fenders f

Berthing Ship, 1 tb ISOPE, pp.583-588.

2. Coastal Development Institute of Technology (1999): Technica

Standards for Port and Harbour Facilities in Japan, pp.48-55.

3. Akakura Yasuhiro et al (1998): Statistical Analysis of Shi

Dimensions for the Size of Design Ship, report of Port an

Harbour Research Institute, No.9 10, ~23.

4. Moriya Kazuyoshi et al (1991): Field Investigation of Approach

Velocity of Berthing Ships, Proceedings of Coastal Engineering

Japan, Vo1.38, pp.751-755.

5. Ueda Shigeru (1981): Study on Berthing Impact Force of Ver

Large Crude Oil Carriers, Report of Port and Harbour Research

Institute, Vo1.20, No.2, pp.169-209.

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Statistical Design of Fender